The auction will be conducted on BSE's e-bidxchange platform from 1530 hours to 1730 hours after close of normal market hours on June 8, the exchange said in a circular today.
The debt auction quota gives overseas investors the right to invest in the debt up to the limit purchased.
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Depository data showed that total investments, including limits acquired by foreign investors through the auction route, stood at Rs 1,21,748 crore till May 14, 97.84% of the total permitted investment limit of Rs 1,24,432 crore in government debt securities.
"BSE will auction investment limits worth Rs 654 crore for overseas investors on Monday i.e, June 8, 2015," the exchange said.
During earlier auctions, government bonds have always been subscribed multiple times, given the huge interest among foreign investors, while the demand for corporate bonds remains less.
Foreign investors are allowed to invest up to USD 25 billion (Rs 1,24,432 crore) in government debt securities through auction while an investment of up to USD 5 billion (Rs 29,137 crore) is permitted 'on tap'.
"The minimum bid is Rs 1 crore and the time period for utilisation of the limits is 15 days from the date of allocation. Upon sale/redemption of debt securities, the FII/QFI will have a re-investment period of 5 days," BSE said.
"If the reinvestment is not made within 5 working days, then the limits shall come back to the pool of free limits."
Last month, NSE had conducted an auction for government bonds worth Rs 2,684 crore, which attracted bids worth Rs 6,657 crore.